Why light has momentum even without mass?

momentum is mass times velocity and light has zero Mass so we would expect its momentum to be zero but that's wrong light happens to have a momentum and its value is e the energy of the light divided by C its speed and I always wondered how did that make any sense I looked up online and I did find some derivation my idea was if I can understand if I can look at the math maybe I can understand the physics boy was I wrong the their derivation starts by saying hey remember Einstein's equation equals mc² and I'm like yes I remember this okay this is interesting then it goes on to say hey eal mc² is not the complete equation Instead This is the complete Einstein's equation and then it says you know what since light has zero Mass just substitute Mass equal to zero and the look what we get we get e s = PC the whole square and the squares cancel out giving you P = e/ c taada yeah that doesn't explain anything so I thought I would never be able to understand where light's momentum comes from where that equation truly comes from until I met finein that's right fan blew my mind away and so by the end of this video we will have a much deeper Insight of why light has momentum even though it has no mass and we'll be able to use that inside to actually derive that equation much more logically but more importantly all by using High School electromagnetism so if you're ready for this let's begin so where do we start well we start by asking finin finin why does light have momentum even though it has zero mass and fin asks back Mahesh why are you so bothered about the fact that something can have momentum even though it doesn't have mass and I tell fan because momentum equals mass time velocity if you don't have mass you won't have momentum and F responds and says ah I see the problem the problem is mahes this is an approximate formula that only works for very special case when things are moving much slower than the speed of light how can you use something like that something so special and generalize it and say that that's what momentum is you see what fan is saying it's kind of like being stuck on an island that only has brown dogs and then thinking that dogs need to be brown in color in fact an animal is only a dog if it is brown in color you see the problem with that right it's only that we have been exposed to brown dogs but in reality dogs have nothing to do with being Brown you can have a white dog you can have any color dog similarly over here just because we're exposed to things that have mass and have momentum we think that that you need to have mass in order to have momentum which need not be the case is the point that fan is making and so where do we go from here well I think we need to take a step back and ask a much bigger question fan what is momentum exactly and fan says that's an excellent question that's an excellent place to start mes so fan says well momentum is the ability to push something and make it move anything that can push something and make it make it move has momentum so if something can push a lot and make it move a lot it has a lot of momentum and if something can push a little bit and make it move a little bit it has a little bit of momentum so let's use this as our definition and then see if light has momentum or not so now the question we need to answer is does light have the ability to push on things and making it move well my first answer is fine with no because light is literally falling on me right now and it's not pushing me at all but F reminds us mes maybe light has very tiny momentum and we just can't feel it so which means we need to either do much more delicate experiments or we need to find a source of light we can find very very powerful source of light luckily we do have a very powerful source of light the Sun and turns out there is something that we can see outside and check whether light has momentum or not comets now I would expect that if a comet is moving this way its tail would be trailing behind it like this but when we look at the comet's tail it turns out to be somewhat like this not trailing behind it feels like it's been blasted away from the Sun what could be making it do that we think it's the light from the sun that's actually blast sting it away look right in front of your eyes there's an example of where light has the ability to push on things and make it move and just to be sure we have now done more careful experiments in our lab where we have shined laser on extremely thin metallic foils on a almost frictionless surfaces and we've found that light can actually push things search for light sails and you will see a lot of those examples so the evidence is right in front of us light has has the ability to push things and make him move and therefore light has momentum but if you're like me you still have the mass issue still not satisfied maybe we can rephrase the question like this fine one for normal day-to-day objects it's their mass that gives them the ability to hit things and push on them and make it move so it's their mass that gives them their momentum right similarly when it comes to light what is it about the light that gives them the ability to push on things and make them move what about light gives it its momentum I think that's a good question and finan says that's an excellent question Mahesh in fact the answer is going to surprise us is what he says and I am intrigued because fan never fails to deliver so let's go feeman what's the answer what makes light have momentum fan says consider an electromagnetic wave traveling to the right we probably already know it has oscillating electric and magnetic fields which are perpendicular to each other and to the direction of light over here I've shown electric field in the vertical plane and the magnetic field over here is in the horizontal plane now fan says consider it is being incident on say a thin foil okay now if you imagine a tiny electron in it that electromagnetic field falls on that elect electron for now let's just focus on the electric field what's going to happen due to the electric field well charged particles experience a force due to the electric field now since electron is negatively charged it's going to experience a force in the opposite direction of the electric field and at this point I'm going to interrupt find one answer I think I get it this is where light's momentum comes from look the electric field is able to push on that electron and make it move and therefore it's transferring momentum to the electron that's where the momentum of light comes from but as I say this I think that doesn't make sense here's the reason why well right now notice the electron is being pushed up and therefore the electron will start moving up but a little later in time the electron will be pushed down and so electron will move down which means on a large enough time interval I will it'll just make the electron go back and forth that's not delivering a net momentum that's not delivering ing anything on the net momentum it delivers is zero so electric field is clearly not delivering the momentum F what are you talking about and fan says yes Mah you're right it's not the electric field that delivers the momentum you interrupted me in it it's in fact the magnetic field it's the magnetic field that's responsible for delivering momentum for light having momentum and I am like well how I mean even magnetic field flips back and forth so even its Force will also flip right and this is where Fineman reminds us to use our high school electromagnetism so let's look at the magnetic force a little bit more carefully if you have a charge that's moving let's say upwards and let's say the magnetic field is coming out of the screen and this is a positive charge then that magnetic field is going to put a force on this charge remember magnetic fields only put force on moving charges and the expression for this force is given by what we we call the Lawrence law now at this point you may be thinking mahes you just bought in a random equation that's not a random equation that's the equation from high school mag electromagnetism just like how electric Fields put a Force Q E magnetic fields put a Force Q we cross B Because velocity matters and for us right now what's important is the direction of the force and the direction of this magnetic force is given by V cross B how do you find that so the way you do that is you use your right hand you you you put your four fingers of the right hand in the direction of the Velocity now over here it's up so you start by pushing it up and then since you are crossing from V to B you curl your fingers towards B now over here since the B is coming out of the screen you curl your fingers towards coming out of the screen and the thumb points to the direction of the magnetic force notice over here the thumb is pointing to the right and therefore the magnetic force over here will be be to the right this is how you find the magnetic force Direction and of course if that's a negative charge like in our case then the force would be in the opposite direction all right so let's apply this and see what is the direction of the force magnetic force acting on the electron over here so to do that let's zoom in a little bit let's start with the first one over here again the velocity is upwards but this time the magnetic field is in two to the page and therefore we Orient our right hand this way look velocity is upwards and now since the magnetic field is into the page we will curl inside and look the thumb points to the left but since it's the electron it's a negatively charged particle the magnetic force will be to the right and this is interesting because now we getting the force in the direction of the electromagnetic wave in the direction in which the light is moving so that's the direction of the force right now but what's going to happen next when the field flips that's the Moment of Truth for us all right here we go now the velocity is downwards and therefore we start with our hand with our four fingers pointing downwards and since the magnetic field now is coming out of the screen we prepare to curl our fingers coming out of the screen and look at the thumb it again points in wards that means the electron since it's a negative charge will again experience a force to the right this means in both the cases the electron is being pushed to the right the magnetic field in this case will always push the electron to the right and since all the electrons of that material is going to get pushed to the right all these forces will add up and now that material will get a net force and that material will move transferring momentum to it and so you see right in front of your eyes what causes momentum what makes light have momentum it's its magnetic field wow this is amazing I find this amazing because usually when we learn about electromagnetic waves if You' have done that we mostly ignore the magnetic fields we always talk about it's electric Fields whether you're learning interference or polarization or or anything else but right in front of us over here magnetic field is always always ignored but here magnetic fields makes a comeback hits the magnetic field that gives light its momentum who would have thought it was there right in front of our eyes I don't know about you but I was pleasantly surprised when I learned about this for the first time all right we're not done yet we have one last thing to do if this is indeed correct the we need to follow that rabbit hole and ask ourselves can we actually get to the equation from this F when can we derive it and fan says yes mahes we can actually go down the rabbit hole see where it leads us and actually see what the equation is for the light's momentum and so if you're ready for it let's do this let's do the last part and let's see if we can derive it where do we start fan well fan says start with the magnetic force that's the one that's delivering the momentum right so what the magnetic force over here is just going to be Q * V into B the strength of the magnetic force the magnitude well and the reason for that is because when you do a cross product you actually have a sign of the angle between the two but so since over here they're perpendicular look velocity is perpendicular to the magnetic field the angle is 90° sin 90 is 1 in simple terms when V and B are perpendicular to each other this cross product just becomes W * B so the magnetic force right now is q q b into e but what is the magnetic field strength of an electromagnetic wave it turns out that the magnetic field strength and the electric field strength they have a very nice relationship for any electromagnetic wave they always follow this relationship this rule that the magnetic field should always be the strength of the electric field divide by C and again at this point you might say Mah you brought in a random equation and findan reminds us that's not a random equation again that comes from high school electromagnetism when you apply Maxwell's equations to electromagnetic waves that is a relationship that you get out of it but more importantly it makes sense to me all all it's saying is that electric and magnetic fields have some kind of a relationship with them and that makes sense just like how they're perpendicular to each other they have to be this is another condition that they have to be magnetic field should always be electric field strength divided by the speed of light and if you look at this equation carefully you see we have QE QE is basically the strength of the electric force acting on the electron which means if you simplify this we basically get the magnetic force equals the electric force into V / C and I like to pause at this moment because this is such a beautiful equation it's telling me a lot of things about that first of all you can see both the magnetic and the electric force acting on this object in one single equation that's nice but secondly we can also see why magnetic force is so much smaller than electric force because of this huge denominator over here it comes from this equation that's one of the reasons why in electromagnetic waves magnetic forces are usually ignored because their effects are much more tiny compared to the electric force yet when it comes to momentum magnetic field makes a comeback anyways we have a derivation to make so where do we go from here fan fan now asks us to look at the numerator much more carefully and what do we see well remember what force into distance is force into distance is basically what work done it is measure of how much energy is transferred into a body so when I push on something I'm transferring energy into it and forcing distance is a measure of how much energy I transfer well what happens if I divide by time if I consider this per second well distance per second is velocity so this is force into velocity and so Force into velocity is basically work done per second which is in other words energy that I'm transferring into an object per second so when I'm pushing something um If I multiply my force and the velocity due to my force on that object I get how much energy I'm transferring every second and look that's what this is this number is basically the energy that the electric field is transferring into that electron per second and so that's what we get and finally how do we go from here to momentum well we remind ourselves well what is force you might know force is rate of change of momentum in other words force is a measure of how quickly you're transferring momentum momentum transfer per second and so look what we've actually derived we've now derived the momentum that the light transfers per second is the same as the energy that it transfers per second divided by C the speed of light and if you cancel out the seconds you get your equation P equal e / C boom there we go fan has delivered but what I find so much more intriguing about this is that I not only have derived it but I understand the incases of it for example I understand that who is delivering energy into that electron it's the electric field that's doing that it's doing that it is the one that's giving the energy to the electron kicking that electron and giving it a speed but once the electron start starts moving magnetic field kicks in and that starts pushing it giving it the momentum that's the kind of intricacy I never got from any other derivation so not only have we seen why light has momentum because of its magnetic field we've also derived it in a much more logical fashion and the hope is that this has put to rest all the lingering questions that we've had about light and momentum and where the equation comes from I've had a amazing time learning and making a video on this and I hope you did too by the way before you go I plan to make a a few more videos on quantum mechanics relativity and all the fun stuff but just by using High School physics and giving a deep physical intuition if that's the kind of stuff you dig Please Subscribe and show your love because I want to see if this works I want to continue doing a lot more videos on it yeah that's about it bye yeah

Channel: FloatHeadPhysics

Views: 378,824

Keywords: floatheadphysics, floatheadphysix, Mahesh Shenoy, Mahesh shenoy khan Academy, Mahesh shenoy physics

Id: bvzr2HbbPC8

Length: 19min 4sec (1144 seconds)

Published: Thu Oct 05 2023